Perhaps the best studied cluster-state based error-correcting code is the RHG lattice.
In the foliated picture, it can be thought of as alternating so-called primal and dual sheets of 2D cluster states that encode the surface code.
This special topology is what leads to fault tolerance: error detection and decoding involve multiple mutually entangled layers at a time.
The RHG lattice serves as a good first candidate to study for our architecture because not only is it universal for MBQC, but it has high fault-tolerant computational error thresholds (\(\lesssim 1\%\) ).
A full fault-tolerant computation can be performed on the RHG lattice with the help of the RHG scheme [1]}, [2]}, [3]}, [4]}.
A schematic of the RHG lattice is presented in fig:pcell.
The details of the full computation on this lattice—state initialization, gate application, measurement, and error correction—will be reviewed and adapted to our architecture in Sec:QEC,sec:FTQC.
<FIGURE>